1. Field of the Invention
This invention relates generally to a method for maintaining a satellite in an orbit, and more particularly to a method of operating a satellite in an earth orbit inclined to its nominal orbit by placing its angular momentum between the normals of its nominal and actual orbits, especially where the satellite is a communications satellite in a near-geosynchronous orbit.
2. Discussion of the Related Art
For certain satellites, such as communication satellites, it is generally desirable to maintain the satellite in an orbit about the earth such that it remains in a rigid location above a specific point on the earth. This type of orbit is referred to as a geosynchronous orbit, and is represented by a distance of approximately 6.61 times the radius r.sub.e of the earth (r.sub.e is approximately equal to 3964 miles, which gives a geosynchronous orbit of about 22,400 miles). This enables a communication beam from the satellite to accurately cover a desirable area, such as a particular country, on the surface of the earth. Any deviations from this orbit will alter the coverage of the beam. To remain in a geosynchronous orbit it is necessary that the satellite's orbit be substantially in the equatorial plane of the earth at this distance. The satellite itself is oriented perpendicular to this plane. Because of these requirements earth's geosynchronous orbit is crowded with a multitude of satellites further making it necessary to maintain the satellite in a specific desirable location in its orbit. Other considerations and advantages of maintaining the satellite in an accurate geosynchronous orbit are well known to those skilled in the art.
A satellite placed in a geosynchronous orbit will experience deviations from the orbit due to certain effects such as gravitational forces from the sun and moon, as well as deviations from variations in the gravitational force of the earth due to its oblateness. These forces tend to move the satellite in both a north/south (N/S) direction, i.e., above and below the equatorial plane, and an east/west (E/W) direction, i.e. left or right on the orbital path. Excursions in the N/S direction are generally more damaging because they tend to move the satellite out of the equatorial plane and into an inclined orbit. Any deviation causing the satellite to direct its antenna away from a subsatellite boresight location (the specific location which the satellite antenna is directed at) tends to alter the coverage of the entire beam thus providing undesirable results. The undesirable results include missed coverage of the entire target, interference with other communication beams, etc. These deviations are magnified by the fact that the beam can be accurately shaped to a desired target area, such as a country. To an observer at the subsatellite location the satellite appears to be moving in a "figure eight" pattern once per sidereal day due to the satellite being in the inclined orbit.
The above mentioned deviations from the desired geosynchronous orbit of the satellite are generally corrected by equipping the satellites with thrusters, well known to those skilled in the art, to maintain the satellite in the equatorial plane and proper spin orientation. These thrusters require certain propellants which obviously must be stored on the satellite from the time the satellite is launched into orbit until the end of the useful life of the satellite. Since the known propellants are relatively heavy, and the satellite has certain weight restrictions to enable it to be launched into orbit, the useful life of the satellite is usually limited by the amount of propellant which can be stored. Consequently, this provides a critical concern in the design of geosynchronous satellites.
Since maintaining the satellite in the equatorial plane requires excessive thruster fuel usage, it has been proposed in the art to enable the satellite to operate in a slightly inclined orbit and alter the angular placement of the satellite to maintain the appropriate direction of the beam.
The potential benefits of a satellite that can operate in a slightly inclined orbit are a useful service life that could be extended by roughly two years per degree of allowable inclination. To achieve this, it has been proposed that the satellite would be initially launched into an inclined orbit that would naturally drift to an equatorial orbit. This is frequently done in any case, when replacement satellites are launched while their predecessors are still useful, to avoid wasting fuel on inclination control before the satellite is needed. When the satellite inclination reaches the level the satellite can handle, it can commence operation. Once it reaches equatorial orbit, it can operate there until fuel is low, then inclination control can be suspended, and the ( satellite will operate until the inclination exceeds the satellite's limit. The added lifetime is the time taken to drift from the inclination limit to the equatorial plane in the beginning, plus the time taken to drift from the equatorial plane to the inclination limit divided by the average inclination drift rate. The drift rate is less than one degree per year, yielding the figure of two years per degree of allowable inclination. Since communication satellite revenues can exceed $100 million per year, the economic value of this added lifetime is considerable. This value is somewhat reduced by the requirement that the ground antennas be able to track the apparent action of the satellite, but many satellite users, especially mobile users such as ships, planes, and trucks, already have this capability.
To understand how to remove or minimize the undesirable antenna/payload pointing deviations attributed above to orbit inclination, it is useful to discuss how satellite orientation is normally maintained. Most geosynchronous satellites stabilize the satellite attitude by providing a bias angular momentum which resists changes in orientation due to external torques transverse to the bias momentum, a quality often termed "gyroscopic stiffness". Properly sized and maintained, the orientation of the bias momentum remains substantially fixed with respect to the fixed stars. Such satellites are called "momentum bias satellites". The momentum bias is usually supplied by one or more momentum or reaction wheels, which spin a large portion of the satellite (as in "dual-spin" satellites), spin the entire satellite, or by other known means. The direction of the bias momentum vector for geosynchronous satellites is usually maintained within a few degrees of perpendicular to the plane of the orbit (orbit normal). When the satellite is in an exact, non-inclined geosynchronous orbit, this direction is also normal to the equatorial plane (equatorial normal).
While the satellite bias momentum resists changes of satellite orientation transverse to the bias momentum, it does not resist rotations about the bias momentum axis. Such rotations are typically corrected by variations in the magnitude of the bias momentum under closed loop control using an attitude sensor and feedback control. Such control is easily provided, and well known to those skilled in the art.
Commonly, the basic momentum bias system described above is not sufficient to point the payload, or communications beam pattern to the desired accuracy, and thus further means are provided to correct the orientation of the payload or communications beam pattern with respect to the orientation provided by the basic bias momentum attitude.
The desired payload orientation can be described with respect to the bias momentum orientation by describing the necessary corrections that would be required to place the payload in the desired orientation by beginning with the payload in the orientation produced by the bias momentum control without further correction, and rotating it sequentially about three mutually perpendicular axes fixed in the payload, these axes being referred to as the yaw, roll and pitch axes. The required correction angles are referred to as the "yaw error", "roll error", and "pitch error", since, when they are non-zero, the payload is not in its desired orientation. When the spacecraft is in a circular, equatorial, geosynchronous orbit, and the satellite attitude is such that the yaw, roll, and pitch errors are zero, the yaw axis is directed from the satellite to the center of the earth, the pitch axis is directed normal to the plane of the orbit, and pointing south, and the roll axis is perpendicular to the other two, pointing in the direction of travel of the spacecraft. For small errors, the order of the rotations is relatively unimportant, and the effects of roll, pitch and yaw error are as follows: a roll error moves the ground location of the communication pattern away from the desired location in a North/South direction, a pitch error results in an East/West error on the ground, and a yaw error results in a rotation of the ground pattern about the line to the satellite. In general, precise definition of the order, sense, and direction of axes used and the assumed starting orientation is required to accurately describe the pointing error, and usage varies.
The description above is sufficient to describe the basic issues and prior art. The roll, pitch, and yaw errors cause all the undesirable results described above under subsatellite boresight deviation, and if too large, reduce or eliminate the economic usefulness of the satellite.
Schemes for providing attitude control for inclined, near-geosynchronous orbits can be classified by how they place the attitude of the nominal bias momentum, and what further corrections of the payload attitude with respect to the bias momentum attitude are performed. The choice of bias momentum attitude produces payload errors in yaw, roll and pitch that vary periodically over the orbit. Typically, the pitch errors produced by slightly inclined orbits are very small, and the concentration has been on reducing the roll and yaw errors. Since payload performance is typically more sensitive to roll errors than to yaw errors, primary emphasis is placed on removing roll errors. In general, however, payload performance is degraded by the presence of all three types of error, and it is most desirable to eliminate all three.
Placing and maintaining the inertial direction of the bias momentum vector in the face of disturbance torques requires that external torques be applied. Many suitable methods are known to the state of the art including the use of thrusters, magnetic torques, and solar sails.
One of the simplest schemes is to place the bias momentum at orbit normal, without further corrections. This results in roll errors on the order of 18% of the orbit inclination angle, and yaw errors equal to the orbit inclination angle.
A refinement of this scheme is to place the satellite bias momentum at an optimum inertial attitude, without further corrections. This method is disclosed in U.S. Pat. No. 4,776,540 to Westerlund, herein incorporated by reference. The Westerlund reference discloses that by placing the bias momentum vector in the plane of equatorial normal and orbit normal of the inclined orbit, offset from orbit normal in the direction away from equatorial normal, roll errors can largely be eliminated for an area of interest. The size of the offset is a function of the location of the area of interest on the earth's surface, but is on the order of 18% of the angle between equatorial normal and orbit normal. This scheme results in a yaw error angle that is slightly larger than the angle of inclination of the orbit.
Another prior art method of maintaining a satellite in an appropriate geosynchronous orbit is maintaining the satellite in equatorial normal, i.e., perpendicular to the equatorial plane of the earth while the satellite is in an inclined orbit. This configuration creates an error that is almost purely in roll. Such a stabilization method is disclosed in U.S. Pat. No. 4,084,772 to Muhlfelder, herein incorporated by reference. Specifically, that patent discloses a transverse momentum wheel incorporated on board the satellite to compensate for roll attitude deviations. The wheel is oriented along an axis parallel to the satellite's yaw axis. This method includes use of a closed loop roll correction system which is updated to correct for roll by a sinusoidal pattern on each orbit of the satellite.
Other prior art methods maintain the bias momentum at equatorial normal, and offset the payload attitude in roll by using a momentum wheel with a roll-axis pivot, as in many RCA (trade name) geosynchronous communications satellites, or by offsetting the communications beam in roll using an antenna gimbal, as in the Hughes Aircraft HS-376 geosynchronous communications satellites. Such systems largely eliminate the roll, pitch and yaw errors induced by orbit inclination when controlled by closed loop control based on ground-based radio beacon signals.
Methods which require placing the satellite's attitude in either the equatorial normal or the orbit normal, thus requiring compensation in the roll direction or yaw direction, respectively, generally require a large gimbal range in the specific direction of compensation. Moreover, movable antennas and the like typically require separate gimbals for each antenna, thus requiring additional components adding to the weight of the satellite.
The paper, "GSTAR III Attitude for Inclined Geostationary Orbit" (AIAA-90-3495-CP), by S. A. Parvez and P. K. Misra, presents a technique where a spacecraft is generally kept orbit normal, with a momentum wheel roll gimbal used to remove the resulting inclination-induced roll errors, while the yaw error is simply ignored. In this case, when the inclinations are large enough that the yaw error inherent in this strategy cannot be tolerated, the yaw error is reduced to an acceptable level by reorienting the bias momentum from orbit normal closer to equatorial normal, until the yaw error is reduced to an acceptable level. This procedure is at the cost of increasing the roll correction. In the event that the roll gimbal range is insufficient to reduce the yaw error to the desired level, the option of reorienting the angular momentum four times daily by thruster maneuvers is discussed.
Some satellites include the capability of correcting attitude in both roll and yaw, simply to meet their non-inclined requirements. Such satellites include those with two-axis gimballed wheels, double vee-wheels, and those with the capability of cheaply and continuously varying the direction of their bias momentum through the use of magnetic or solar torques. The prior art, which applies corrections in at most a single axis, limits the correctable inclination to the means available about a single axis: e.g., gimbal angle, maximum transverse roll momentum bias, or yaw magnetic or solar torque. The other axis capability is unused. An object of the present invention is to maximize the orbit inclination capability of such satellites by using the actuation range available in both roll and yaw axes. Since communication satellite revenues can exceed $10 million per month, and the potential added life is greater than 1 month per 0.05 degrees of allowable inclination, the capability to handle even a few extra tenths of a degree of inclination has considerable economic value.